Modeling elastic beams using dynamic splines

In this paper, the authors present the description and an application of the theory of dynamic splines for the modeling of very flexible beams in multibody systems. The use of spline formalism reveals an alternative method for the description of continuum flexibility by using discrete parameters. The proposed approach is discussed in general terms and a specific example is presented and compared to nonlinear finite element simulation.

[1]  E. Haug,et al.  Geometric non‐linear substructuring for dynamics of flexible mechanical systems , 1988 .

[2]  J. Gerstmayr,et al.  A 3D Finite Element Method for Flexible Multibody Systems , 2006 .

[3]  A. Shabana Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation , 1997 .

[4]  Hong Qin,et al.  D-NURBS: A Physics-Based Framework for Geometric Design , 1996, IEEE Trans. Vis. Comput. Graph..

[5]  Alberto Cardona Superelements Modelling in Flexible Multibody Dynamics , 2000 .

[6]  A. Shabana,et al.  DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION , 2000 .

[7]  T.J.A. Agar,et al.  Geometric nonlinear analysis of flexible spatial beam structures , 1993 .

[8]  Ashitava Ghosal,et al.  Comparison of the Assumed Modes and Finite Element Models for Flexible Multilink Manipulators , 1995, Int. J. Robotics Res..

[9]  Michał Kleiber,et al.  Computational aspects of nonlinear structural systems with large rigid body motion , 2001 .

[10]  Laurent Grisoni,et al.  Adaptive resolution of 1D mechanical B-spline , 2005, GRAPHITE '05.

[11]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[12]  M. Géradin,et al.  Flexible Multibody Dynamics: A Finite Element Approach , 2001 .

[13]  Stefan von Dombrowski,et al.  Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates , 2002 .

[14]  Peter Eberhard,et al.  Flexible Multibody Systems with Large Deformations and Nonlinear Structural Damping Using Absolute Nodal Coordinates , 2003 .

[15]  J. C. Samin,et al.  Nonlinear Dynamic Model of a System of Flexible Bodies Using Augmented Bodies , 1998 .

[16]  Stephane Cotin,et al.  Interactive physically-based simulation of catheter and guidewire , 2006, Comput. Graph..

[17]  Ahmed A. Shabana,et al.  Flexible Multibody Dynamics: Review of Past and Recent Developments , 1997 .

[18]  Daniel García-Vallejo,et al.  Study of the Geometric Stiffening Effect: Comparison of Different Formulations , 2004 .

[19]  E. Haug,et al.  Selection of deformation modes for flexible multibody dynamics , 1987, DAC 1987.

[20]  K. Hsiao,et al.  A CO-ROTATIONAL FORMULATION FOR NONLINEAR DYNAMIC ANALYSIS OF CURVED EULER BEAM , 1995 .

[21]  Ahmed A. Shabana,et al.  On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation , 2009 .

[22]  J. C. Simo,et al.  On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part II , 1986 .

[23]  I. Sharf GEOMETRICALLY NON‐LINEAR BEAM ELEMENT FOR DYNAMICS SIMULATION OF MULTIBODY SYSTEMS , 1996 .

[24]  Zhuyong Liu,et al.  Finite element formulation for dynamics of planar flexible multi-beam system , 2009 .

[25]  Johannes Gerstmayr,et al.  On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach , 2008 .

[26]  Laurent Grisoni,et al.  Geometrically exact dynamic splines , 2008, Comput. Aided Des..

[27]  Jean-Claude Samin,et al.  Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics , 1997 .